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Consider the Orlicz spaces $L^A(\mathbb{R}^n)$. Under suitable conditions for the $N$-function $A(x,t)$, namely $(Inc)_p$, $(Dec)_q,$, for $1<p<q<\infty$, it is known that $$L^p\cap L^q \subset L^A\subset L^p+L^q,$$ i.e., from the point of view of interpolation theory it is an intermediate space for the couple $(L^p,L^q)$. Real interpolation of Lebesgue spaces yields Lorentz spaces, however the fact from Orlicz spaces made me wonder if there is a known result connecting $L^A$ with the general real interpolation method applied to $(L^p,L^q)$, where the function $t^\theta$ is replaced by more general function $\rho(t)$ in the definition of the norm of the interpolation space. Summing up, is there any result like $(L^p,L^q)_{\theta,q,\rho}=L^A,$?

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